Medical lines of various types are typically present in the clinical setting in connection with institutional and at-home care for patients. Medical lines can include intravenous lines used for the delivery of fluids, blood, and therapeutic and prophylactic agents, device monitoring lines, feeding tubes, and tubes for delivery of gas, such as oxygen. Such lines are affixed to the patient at a first end and to a medical device, such as an infusion pump, monitor, or valve at a second end. The length of the line is typically sufficient to allow for some range of movement of the patient away from the medical device, and most medical lines are flexible. Thus, such lines commonly become intertwined, leading to the risks of confusion and damage to the lines or to the patient or equipment. Further, such lines are likely to be contaminated by contact with the floor, the patient bed, persons in the patient room, and devices near the patient, thus increasing the risk of the entry into the patient of pathogens. Moreover, in many instances, such medical lines are prone to entanglement with the patient. In most circumstances, the harm associated with such entanglement is kinking or breakage of the medical line, or disengagement from the patient or the medical device, or some other form of damage to medical equipment. In some more unfortunate circumstances, entanglement with the patient can lead to patient injury or death by asphyxiation. This is a more significant concern with pediatric patients and with disabled or unconscious patients. Thus, there is a need for devices and methods for securing medical lines so as to minimize the risk of dangerous entanglement with patients, and to minimize the likelihood of confusion between medical lines and line contamination.